In meter bridge, an unknown resistance X has specific resistance $S_1=\frac{X\mathrm{\pi <!--\; \pi \; -->}{R}^2}{I},$ where R is radius and l is length. If length and radius both are doubled, new specific resistance is

The correct option is S₁.

Let us analyze the logical reasoning behind this result step-by-step.
Specific resistance, also known as resistivity, is a fundamental characteristic property of the material of a conductor. It depends strictly on the nature of the material of the conductor and its temperature.

Mathematically, the relationship is given as:
$S_1=\frac{X\pi R^2}{l}$
Here, $X$ is the resistance, $R$ is the radius of the wire, and $l$ is the length of the wire.

When the physical dimensions of the wire (such as its length and radius) are doubled, the resistance $X$ changes, but the material of the wire remains the same.
Because specific resistance (resistivity) is an intrinsic material property, it does not depend on the length, radius, or shape of the wire. Therefore, changing the length and radius of the wire has no effect on its specific resistance.

Thus, the new specific resistance remains equal to the original specific resistance, which is $S_1$.